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Display and Compare Two Proper Fractions

Display and Compare Two Proper Fractions
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2013-06-05 04:32
SequenceTransformationGeometric Construction
In collections fifth grade fractions
This example demonstrates multiple representations of two different proper fractions, including linear, number line, and set models. Students can better understand the concept of proper fractions and their geometric meanings through these different representations. The construction uses commands such as Point, Min, If, Vector, Rotate, CircleSector, Segment, Polygon, Sequence, Circle, and FractionText in GeoGebra. Suitable for students from upper elementary to middle school, it helps develop students' geometric intuition and mathematical thinking.

GeoGebra Commands & Parameters

  1. Point(Circle[R_1, 0.12]) → C_2
  2. Min(9 / denom1, 1) → a9
  3. Min(4 / denom1, 1) → a4
  4. Min(5 / denom1, 1) → a5
  5. Min(8 / denom1, 1) → a8
  6. Min(7 / denom1, 1) → a7
  7. Min(6 / denom1, 1) → a6
  8. Min(1 / denom1, 1) → a1
  9. Min(2 / denom1, 1) → a2
  10. If(denom1 < 10, " " + denom1, "" + denom1) → formatd
  11. Min(3 / denom1, 1) → a3
  12. Min(10 / denom1, 1) → a10
  13. Point(Circle[M, 1]) → Q
  14. Point(Circle[N, 1]) → R
  15. Point(Circle[L_1, 0.02]) → U_1
  16. Point(Circle[U_1, 0.5]) → V_1
  17. If(impr > 1, 1, 0) → Rect_{show}
  18. Vector(NL_c, NL_l) → u
  19. Vector(NL_c, NL_r) → v
  20. If(num1 / denom1 > 1, 1, 0) → Set_{show}
  21. Rotate(C_2, angle, R_1) → D_2
  22. CircleSector(R_1, C_2, D_2) → circle1_{sector}
  23. Rotate(C_2, (360 / denom1)°, R_1) → B_2
  24. Segment(K_2, L_2) → a_2
  25. Vector((0, 0.25), (0.1, 0.25)) → image_{vector}
  26. Polygon((0, 0.38), ((0.5 * num1 / denom1), 0.38), ((0.5 * num1 / denom1), 0.58), (0, 0.58)) → frac1area3_{shaded}, j_1, k_1, l_1, m_1
  27. Segment((1, 0.43), (1, 0.47)) → i_2
  28. Sequence(Segment[((1 / frac1linediv * i), 0.43), ((1 / frac1linediv * i), 0.47)], i, 1, frac1linediv) → frac1numLineHash
  29. Segment((0, 0.42), (0, 0.48)) → t_1
  30. Segment((1, 0.42), (1, 0.48)) → a
  31. Polygon((0, 0.38), (num1 / 10, 0.38), (num1 / 10, 0.58), (0, 0.58)) → frac1area2_{shaded}, b, c, d, e
  32. Sequence(Segment[(i / denom1, 0.42), (i / denom1, 0.48)], i, 1, denom1 - 1) → frac1linearModelDivisions
  33. Polygon((0, 0.42), (num1 / denom1, 0.42), (num1 / denom1, 0.48), (0, 0.48)) → frac1linear_{shaded}, f, g, h, i
  34. Sequence(Translate[Circle[(0.05, 0.48), 0.045], Vector[(0, 0), ((0.1 * i), 0)]], i, 0, denom1 - 1) → frac1OpenCircles
  35. Sequence(Translate[Circle[(0.05, 0.48), 0.04], Vector[(0, 0), ((0.1 * i), 0)]], i, 0, num1 - 1) → frac1setClosed
  36. Sequence(Segment[Rotate[(0.1504, 0.2), (360 / denom1)°, (0.1504, 0.2)], Rotate[(0.1504, 0.31), ((360 * i) * ° / denom1), (0.1504, 0.2)]], i, 0, denom2 - 1) → Circle2_{model-divisions}
  37. Circle((0.15, 0.2), 0.12) → Circle2_{outline}
  38. Sequence(Segment[Rotate[(0.15, 0.2), ((360 / denom1 * i))°, (0.15, 0.2)], Rotate[(0.15, 0.32), ((360 * i / denom2))°, (0.15, 0.2)]], i, 0, denom2) → circle2_{div}
  39. Circle((0.15, 0.475), 0.12) → Circle1_{outline}
  40. Sequence(Segment[Rotate[(0.15, 0.475), ((360 / denom1 * i))°, (0.15, 0.475)], Rotate[(0.15, 0.595), ((360 * i / denom1))°, (0.15, 0.475)]], i, 0, denom1) → circle1_{div}
  41. CircleSector((0.15, 0.2), (0.15, 0.32), Rotate[(0.15, 0.32), ((360 * num2 / denom2))°, (0.15, 0.2)]) → p
  42. Polygon((0, 0.38), (denom1 / 10, 0.38), (denom1 / 10, 0.58), (0, 0.58)) → frac1area2_{outline}, r, s, t, a_1
  43. Sequence(Segment[(i / 10, 0.38), (i / 10, 0.58)], i, 1, denom1 - 1) → frac1area_{div}
  44. Polygon((0, 0.1), (denom2 / 10, 0.1), (denom2 / 10, 0.3), (0, 0.3)) → frac2area2_{outline}, j, l, n, q
  45. Sequence(Segment[(i / 10, 0.1), (i / 10, 0.3)], i, 1, denom2 - 1) → frac2area_{div}
  46. Polygon((0, 0.1), (num2 / 10, 0.1), (num2 / 10, 0.3), (0, 0.3)) → frac2area2_{shaded}, b_1, c_1, d_1, e_1
  47. Polygon((0, 0.38), (0.5, 0.38), (0.5, 0.58), (0, 0.58)) → frac1area3_{outline}, f_1, g_1, h_1, i_1
  48. Polygon((0, 0.1), (0.5, 0.1), (0.5, 0.3), (0, 0.3)) → frac2area3_{outline}, n_1, p_1, q_1, r_1
  49. Sequence(Segment[((0.5 / denom1 * i), 0.38), ((0.5 / denom1 * i), 0.58)], i, 1, denom1 - 1) → frac1area3_{div}
  50. Sequence(Segment[((0.5 / denom2 * i), 0.1), ((0.5 / denom2 * i), 0.3)], i, 1, denom2 - 1) → frac2area3_{div}
  51. Polygon((0, 0.1), ((0.5 * num2 / denom2), 0.1), ((0.5 * num2 / denom2), 0.3), (0, 0.3)) → frac2area3_{shaded}, s_1, b_2, c_2, d_2
  52. Sequence(Translate[Circle[(0.05, 0.2), 0.04], Vector[(0, 0), ((0.1 * i), 0)]], i, 0, num2 - 1) → frac2setClosed
  53. Sequence(Translate[Circle[(0.05, 0.2), 0.045], Vector[(0, 0), ((0.1 * i), 0)]], i, 0, denom2 - 1) → frac2setOpen
  54. Vector(NL_c + (0, -0.27), NL_l + (0, -0.27)) → u_1
  55. Vector(NL_c + (0, -0.27), NL_r + (0, -0.27)) → v_1
  56. Segment((0, 0.43), (0, 0.47)) → f_2
  57. Segment((0, 0.16), (0, 0.2)) → e_2
  58. Segment((1, 0.16), (1, 0.2)) → g_2
  59. Sequence(Segment[((1 / frac2linediv * i), 0.16), ((1 / frac2linediv * i), 0.2)], i, 1, frac2linediv) → frac2numLineHash
  60. Vector(Frac2NumLnPt + (0, 0.05), Frac2NumLnPt) → frac2NumLnPtVector
  61. Vector(Frac1NumLnPt + (0, 0.05), Frac1NumLnPt) → frac1NumLnPtVector
  62. FractionText(1 / frac2linediv) → model2NumLnIntervalValue
  63. FractionText(1 / frac1linediv) → model1NumLnIntervalValue
  64. Segment(K_2 + (0, -0.27), L_2 + (0, -0.27)) → h_2
  65. Sequence(Segment[(i / denom2, 0.15), (i / denom2, 0.21)], i, 1, denom2 - 1) → frac2linearModelDivisions
  66. Segment((1, 0.15), (1, 0.21)) → j_2
  67. Segment((0, 0.15), (0, 0.21)) → k_2
  68. Polygon((0, 0.15), (num2 / denom2, 0.15), (num2 / denom2, 0.21), (0, 0.21)) → frac2linear_{shaded}, l_2, m_2, n_2, p_2
  69. Sequence(Polygon[(-0.455, 0.117 + k), (-0.195, 0.117 + k), (-0.195, 0.31 + k), (-0.455, 0.31 + k)], k, 0, 0.276, 0.276) → grayBoxes
  70. Sequence(Segment[(-0.435, 0.189 + k), (-0.397, 0.189 + k)], k, 0, 0.276, 0.276) → fracVinculum

AI Drawing Prompt Reference

Draw multiple representations of two proper fractions, including set models, linear models, and geometric models. Start by drawing two circles to represent the set models of the fractions. Then, draw two number lines to represent the linear models of the fractions. Next, draw two sectors to represent the geometric models of the fractions. Finally, use rectangles and polygons to shade the areas corresponding to each fraction.
The prompt above was compiled from the original drawing commands and is for reference only.